A factor of safety of 2.5 is used for the bolts in the assembly below. The ultimate shear stress of the magnesium alloy bolts is 20.0ksi. What should be the diameter of the bolts? 10 kip 5 kip 3 kip
Design Against Fluctuating Loads
Machine elements are subjected to varieties of loads, some components are subjected to static loads, while some machine components are subjected to fluctuating loads, whose load magnitude tends to fluctuate. The components of a machine, when rotating at a high speed, are subjected to a high degree of load, which fluctuates from a high value to a low value. For the machine elements under the action of static loads, static failure theories are applied to know the safe and hazardous working conditions and regions. However, most of the machine elements are subjected to variable or fluctuating stresses, due to the nature of load that fluctuates from high magnitude to low magnitude. Also, the nature of the loads is repetitive. For instance, shafts, bearings, cams and followers, and so on.
Design Against Fluctuating Load
Stress is defined as force per unit area. When there is localization of huge stresses in mechanical components, due to irregularities present in components and sudden changes in cross-section is known as stress concentration. For example, groves, keyways, screw threads, oil holes, splines etc. are irregularities.
![### Determining Bolt Diameter for Safety in Structural Assemblies
#### Problem Description:
A factor of safety of 2.5 is used for the bolts in the assembly shown below. The ultimate shear stress of the magnesium alloy bolts is 20.0 ksi. What should be the diameter of the bolts?
#### Assembly Diagram:
- **Description:** The diagram shows a three-layered assembly held together by a bolt.
- **Forces:**
- A leftward force of 10 kip is applied on the left side of the top layer.
- Two rightward forces of 5 kip each are applied on the lower layers.
#### Calculation Objective:
Determine the appropriate diameter for the bolts to ensure structural integrity and safety.
#### Solution Steps:
1. **Determine Allowable Shear Stress:**
- Calculate the allowable shear stress using the ultimate shear stress and the factor of safety.
2. **Calculate Required Bolt Area:**
- Use the allowable shear stress to determine the required cross-sectional area of the bolt.
3. **Find Bolt Diameter:**
- Use the area to find the necessary diameter of the bolt.
#### Result:
- **Diameter = __________ in**
Please fill in the computed diameter based on the provided data and calculations.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa572c903-8f29-4a18-ba49-8181d6c8cb85%2F9de86732-bd34-4892-bd21-1baa29355842%2F1or1f4m_processed.png&w=3840&q=75)
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